Preheat a grill to medium and position a large cast-iron skillet off to the side. On a 12-inch sheet of foil, toss the wet green beans with 1 tablespoon olive oil and season with salt and pepper; wrap tightly to enclose. Once the skillet is hot, add the bacon to the pan in an even layer and place the packet of green beans on the cooking grate. Cook the bacon, turning once, until crisp, about 7 minutes; drain on paper towels and then crumble. Remove the packet from the grill and open to let the beans cool. Carefully remove the skillet from the grill.
Brush the polenta slices on both sides with the remaining 3 tablespoons olive oil. Arrange on the cooking grate, cover and grill, turning once, until toasted, about 5 minutes. Using a spatula, transfer the polenta slices to a work surface.
Spread the mustard on one side of 8 polenta slices, then layer each with 1 tablespoon cheese, 1 tomato slice, another tablespoon cheese, some of the bacon and another tablespoon cheese. Set the remaining polenta slices in place to make 8 sandwiches. Using the same spatula, carefully transfer the stacks onto the cooking grate, cover and grill until the cheese is melted, about 2 minutes. Serve with the green beans.